Answer:
The domain of f is equal to x = log8 x.
Step-by-step explanation:
Find the value of x.
Step-by-step explanation:
3x-12 + 6 = 14
3x-12 = 14 - 6
3x = 8 + 12
x= 20 ÷ 3
x = 6.7
Internal Angle Bisector Theoram:
Interior Angle Bisector Theorem : The angle bisector of an angle of a triangle divides the opposite side internally in the ratio of the sides containing the angle.
[tex] \Large{ \boxed{ \bf{ \color{limegreen}{Solution:}}}}[/tex]
Here, We can see that angle bisector of an angle is dividing the opposite side.
And,
From here, we can say that the ratio of side being divided is same as the ratio of sides containing this angle.
So, we can write it as,
➝ 14 : 21 = 6 : 3x - 12
Prdouct of means = Product of extremes
➝ 21 × 6 = 14(3x -12)
➝ 126 = 14(3x - 12)
➝ 9 = 3x - 12
Flipping it,
➝ 3x - 12 = 9
➝ 3x = 21
➝ x = 7
☘️ So, Value of x is [tex]\boxed{\sf{x = 7}}[/tex]
━━━━━━━━━━━━━━━━━━━━
How to translate the number of people increased by 13 into an algebraic expression
Answer:
x +13.
where
x is number of people
Step-by-step explanation:
Let the number of people be x
given that number of people increased by 13
increased by 13 means that we whatever is the initial number of people, new number of people is 13 more than that.
thus, new number of people = x +13
to translate the number of people increased by 13 into an algebraic expression
we add 13 to number of people which can be represented by x +13.
A newsletter publisher believes that above 41A% of their readers own a personal computer. Is there sufficient evidence at the 0.100.10 level to substantiate the publisher's claim?
Complete Question
A newsletter publisher believes that above 41% of their readers own a personal computer. Is there sufficient evidence at the 0.10 level to substantiate the publisher's claim?
State the null and alternative hypotheses for the above scenario.
Answer:
The null hypothesis is [tex]H_o : p \le 0.41[/tex]
The alternative hypothesis [tex]H_1 : p> 0.41[/tex]
Step-by-step explanation:
From the question we are told that
The population proportion is [tex]p = 0.41[/tex]
The level of significance is [tex]\alpha = 0.10[/tex]
The null hypothesis is [tex]H_o : p \le 0.41[/tex]
The alternative hypothesis [tex]H_1 : p> 0.41[/tex]
s=πrl+πr2 solve for l.
Answer:
[tex]l = \frac{s - π {r}^{2} }{πr} [/tex]Step-by-step explanation:
s = πrl + πr²
First move πr² to the left side of the equation
We have
πrl = s - πr²
Divide both sides by πr to make l stand alone
That's
[tex] \frac{\pi \:rl}{\pi \: r} = \frac{s - \pi \: {r}^{2} }{\pi \: r} [/tex]We have the final answer as
[tex]l = \frac{s - π {r}^{2} }{πr} [/tex]Hope this helps you
Use technology and a t-test to test the claim about the population mean at the given level of significance using the given sample statistics. Assume the population is normally distributed. Claim: ; Sample statistics: , s, n What are the null and alternative hypotheses? Choose the correct answer below. A. H0: HA: B. H0: HA: C. H0: HA: D. H0: HA:
Complete question is;
Use technology and a t-test to test the claim about the population mean μ at the given level of significance α using the given sample statistics. Assume the population is normally distributed.
Claim: μ > 71; α = 0.05
Sample statistics:
¯x = 73.9, s = 3.7, n = 25
A) What are the null and alternative hypotheses?
Choose the correct answer below.
A. H0:μ = 71 ; HA:μ ≠ 71
B. H0:μ ≤ 71; HA:μ > 71
C. H0: μ ≥ 71; HA: μ < 71
D. H0: μ ≠ 71; HA: μ = 71
B) What is the value of the standardized test statistic? The standardized test statistic is (Round to two decimal places as needed.)
C) What is the P-value of the test statistic? P-value = Round to three decimal places as needed.)
D) Decide whether to reject or fail to reject the null hypothesis.
Answer:
A) Option B - Alternative hypothesis: HA: μ > 71
Null hypothesis: H0: μ ≤ 71
B) t = -7.54
C) p-value = 0.000
D) we reject the null hypothesis
Step-by-step explanation:
A) We are told that the claim is: μ > 71. Thus, due to the sign, the alternative hypothesis would be the claim. So;
Alternative hypothesis: HA: μ > 71
Null hypothesis: H0: μ ≤ 71
B)Formula for standardized test statistic with a t-test is;
t = (¯x - μ)/√(s/n)
Plugging in the relevant values, we have;
t = (71 - 73.9)/√(3.7/25)
t = -7.54
C) From online p-value from t-score calculator attached using t = -7.54, n = 25, significance level = 0.05, DF = 25 - 1 = 24 and a one - tailed test, we have;
p-value = 0.00001 ≈ 0.000
D) The p-value of 0.000 is less than the significance value of 0.05,thus we will reject the null hypothesis
Celine's book club read 42 books over 14 months. How many total months will it take them to read 57 books? Solve using unit rates.
Answer:
Step-by-step explanation:
42/14 = 57/x
42x = 57*14
42x = 798
x = 19 months
Answer: Actually its 18 months they calculated wrong
When air expands adiabatically (without gaining or losing heat), its pressure P and volume V are related by the equation
PV^1.4=C
where C is a constant. Suppose that at a certain instant the volume is 610 cubic centimeters and the pressure is 89 kPa and is decreasing at a rate of 10 kPa/minute. At what rate in cubic centimeters per minute is the volume increasing at this instant?
Answer:
48.96 cm³/min
Step-by-step explanation:
We are given;
Relationship between pressure P and volume V; PV^(1.4) = C
Volume;V = 610 m³
Pressure; P = 89 KPa
Rate of decreasing pressure; dP/dt = -10 kPa/minute.
We want to find the rate at which the volume is increasing at that instance, thus, its means we need to find dV/dt
So, we will differentiate the relationship equation of P and V given.
Thus, we have;
[V^(1.4)(dP/dt)] + d(V^(1.4))/dt = dC/dt
Differentiating this gives us;
[(dP/dt) × (V^(1.4))] + [1.4 × P × V^(0.4) × (dV/dt)] = 0
Plugging in the relevant values, we have;
(-10 × 610^(1.4)) + (1.4 × 89 × 610^(0.4) × (dV/dt)) = 0
This gives;
-79334.44155 + 1620.5035(dV/dt) = 0
Rearranging, we have;
1620.5035(dV/dt) = 79334.44155
Divide both sides by 1620.5035 to give;
dV/dt = 79334.44155/1620.5035
dV/dt = 48.96 cm³/min
Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y. Draw a typical approximating rectangle.
2x + y2 = 48, x = y
Find the area of the region.
Answer: A = 58
Step-by-step explanation: The sketched region enclosed by the curves and the approximating rectangle are shown in the attachment.
From the sketches, the area will be integrated with respect to y.
To calculate the integral, first determine the limits, which will be the points where both curves meet.
In respect to y:
[tex]2x+y^{2} = 48[/tex]
[tex]2x= 48- y^{2}[/tex]
[tex]x= 24 - \frac{y^{2}}{2}[/tex]
Finding limits:
[tex]y= 24 - \frac{y^{2}}{2}[/tex]
[tex]24 - \frac{y^{2}}{2}-y=0[/tex]
Multiply by 2 to facilitate calculations:
[tex]48 - y^{2}-2y=0[/tex]
Resolving quadratic equation:
[tex]y=\frac{-2+\sqrt{2^{2}+192} }{2}[/tex]
y = 6 and y = -8
Then, integral to calculate area will be with limits -8<y<6:
[tex]A = \int {24-\frac{y^{2}}{2}-y } \, dy[/tex]
[tex]A = 24y - \frac{y^{3}}{6}-\frac{y^{2}}{2}[/tex]
[tex]A = 24.6 - \frac{6^{3}}{6}-\frac{6^{2}}{2}-[24.(-8) - \frac{(-8)^{3}}{6}-\frac{(-8)^{2}}{2}][/tex]
A = 58
The area of the enclosed region is 58 square units.
Find the average rate of change of the area of a circle with respect to its radius r as r changes from 3 to each
Answer:
Step-by-step explanation:
The question is incomplete. Here is the complete question.
Find the average rate of change of the area of a circle with respect to its radius r as r changes from 3 to each of the following.
(i) 3 to 4
(ii) 3 to 3.5
(iii) 3 to 3.1
(b) Find the instantaneous rate of change when r = 3. A'(3)
Area of a circle A(r)= πr²
The average rate of change of the area of a circle with respect to its radius
ΔA(r)/Δr = πr₂²-πr₁²/r₂-r₁
ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁
i) If the radius changes from 3 to 4
ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁
ΔA(r)/Δr = π(4²-3²)/4-3
ΔA(r)/Δr = π(16-9)/1
ΔA(r)/Δr = 7π
Hence, average rate of the area of a circle when the radius changes from 3 to 4 is 7π
ii) If the radius changes from 3 to 3.1
ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁
ΔA(r)/Δr = π(3.5²-3²)/3.5-3
ΔA(r)/Δr = π(12.25-9)/0.5
ΔA(r)/Δr = 3.25π/0.5
ΔA(r)/Δr = 6.5π
Hence, average rate of the area of a circle when the radius changes from 3 to 3.5 is 6.5π
iii) If the radius changes from 3 to 3.1
ΔA(r)/Δr = π(r₂²-r₁²)/r₂-r₁
ΔA(r)/Δr = π(3.1²-3²)/3.1-3
ΔA(r)/Δr = π(9.61-9)/0.1
ΔA(r)/Δr = 0.61π/0.1
ΔA(r)/Δr = 6.1π
Hence, average rate of the area of a circle when the radius changes from 3 to 3.1 is 6.1π
iv) Instantaneous rate of change A'(r) = 2πr
When r = 3;
A'(3) = 2π(3)
A'(3) = 6π
Hence, the instantaneous rate of change when r = 3 is 6π
Answer:A number decreased by 4 is the same as 12.5
Step-by-step explanation:
The following data shows the number of laps run by each participant in a marathon. 46 65 55 43 51 48 57 30 43 49 32 56Which of these choices display the correct stemplot?A. 3 0 2 4 3 6 8 9 4 1 3 5 6 7 6 5B. 3 0 2 4 3 3 6 8 9 5 1 5 6 7 6 5
Answer:
The Stem plot is displayed below.
Step-by-step explanation:
A Stem Plot is a chart for demonstrating the distribution of numeric variables .
It is used to analyze the shape of the distribution.
The data provided is as follows:
S = {46, 65, 55, 43, 51, 48, 57, 30, 43, 49, 32, 56}
The Stem plot is displayed as follows:
3 | 0 2
4 | 3 3 6 8 9
5 | 1 5 6 7
6 | 5
4.72x10^10 Please I need help fast
Answer:
The answer is 47200000000
1. Type your answer below. 2. Type your answer below (no spaces! for example x=19) 3. Type your answer below (no spaces! for example x=19) Need help with all three answers please quick
Answer:
1) 12
2) c=-25
3) x = -16 2/3
Step-by-step explanation:
1) ..........................
6*(4-10+8) =6*(- 6+8) =6*2= 122) ..........................
34 + 2c = -162c = - 16 -342c = -50c = -50/2c=-253) ..........................
40 = -3x - 1040+ 10 = -3x-3x = 50x = 50/-3x=-16 2/3Given A = {a, b, c, d} and B = {1, 2, 3, 4} , sets A and B can be defined as? Question 2 options: equal sets equivalent sets equal and equivalent sets neither equal or equivalent sets
Answer:
equal and equivalent sets
Step-by-step explanation:
1. Brandon has $12. He will eam $8 for every
hour he works. He would like to have $52 at
the end of the day. Let h represent the
number of hours Brandon works.
Equation:
Solve it to find how many hours he needs
Answer:52-12=$40
1/8*40 = 5 hours.
Step-by-step explanation:
Choose two statements that are true for this expression.
4x^3 – 7x^2 – 30/y + 15
A. There are four terms.
B. There are three terms. 30
C. The term is a ratio.
D. The entire expression is a difference.
Answer:
A. There are four terms.
C. The term [tex]\frac{30}{y}[/tex] is a ratio.
Step-by-step explanation:
The expression given is the sum of four components: a third order monomial ([tex]4\cdot x^{3}[/tex]), a second order monomial ([tex]-7\cdot x^{2}[/tex]), a zero order monomial ([tex]15[/tex]) and a ratio ([tex]\frac{30}{y}[/tex]). There are a sum and two differences. Hence, the correct answers are:
A. There are four terms.
C. The term [tex]\frac{30}{y}[/tex] is a ratio.
Answer:
there are 4 terms
the term 30/y is a ratio
Step-by-step explanation:
got it right on my quiz
Where does the graph of the line 3x – 4y = 12 intersect the y-axis?
A. (4,0)
B. (-4, 0)
C. (0, 3)
D. (0, -3)
Answer
[0,-3] should be the right answer
The line should intersect at y axis i.e x=0
Then put the value of x as zero in the equation to find the value of y.
3*0-4y=12
-4y=12
y=12/-4=-3
y=-3 ..
HOPE THIS HELPS YOU
Eddie treated his sister to lunch while visiting her in Manchester, Their lunch cost $20, and the
sales tax in Manchester is 15%, If Eddie left a 15% tip on the $20, how much in total did he pay?
Sul
Answer:
Eddie spent $26 total
Step-by-step explanation:
15% of 20 is 3
He paid 15% tax which is $3
He also tipped 15% of the $20 which he paid for lunch so another $3
3+3+20= $26
answer the following Question
Answer:
a)$15.95
b) 8kg
Step-by-step explanation:
a)Approach this question by finding how much does it cost for 1g
So,
$2.1/50=$0.042per gram
then, multiple 380 to get the cost of sweets for 380 g
$0.042/gram*380gram=$15.96(Note: the gram cancel out each other)
Which is $15.95 as the question requested
b)This question stated that 3/4 of the metal has 15 kg
So, in order to find the total mass of metal we invert the 3/4 fraction
e.g 4/3*15=20kg
now we have the total mass we can find the mass for 2/5 of the metal
2/5*20kg=8kg
Calculate the mean deviation by median (by using the mid-point(x) of leaf weights. b) A fair die is rolled. Find the probability of getting an odd number or a prime number or both?
Answer:
hello attached below is the required table that is missing and the completed table as well
A) mean deviation = 0.1645
B) 2/3
Step-by-step explanation:
From the table we calculated the midpoint value (x) and c.f
N = 27
median class = 2.35 to 2.45
median = l + [ (N/2) - cf / F ] * H
= 2.35 + [ (13.5 - 13) / 6 ] *0.1 = 2.3583
hence mean deviation by median
= summation of fi |xi -M| / summation of fi
= 4.4417 / 27 = 0.1645
B ) probability of getting an odd number or prime number or both
the probability of an odd number = 1/2
also the probability of an even number = 1/2
while the probability of getting neither of them = 1/3
hence the probability of getting odd or prime or both
= 1/2 + 1/2 - 1/3 = 2/3
what percent of 6.2 is 14
Answer:
0.87
Step-by-step explanation:
Derivative Function.. Could you solve this, please?
Hello, please consider the following.
f is differentiable so g is differentiable and we we can compute the derivative of g.
[tex]\text{derivative of } u^2\text{ is } 2uu'\\\\\text{derivative of } f(f(x^3)+x)\text{ is } (3x^2f'(x^3)+1)f'(f(x^3)+x)\\\\\text{So, }\\\\g'(x)=2f(f(x^3)+x)(3x^2f'(x^3)+1)f'(f(x^3)+x)\\\\\text{ We replace x par 1}\\\\g'(1)=2f(f(1)+1)(3f'(1)+1)f'(f(1)+1)\\\\g'(1)=2f(2)(3f'(1)+1)f'(2)\\\\\text{ We can put f'(2) in one part of the equation}\\\\f'(2)=\dfrac{2f(2)(3f'(1)+1)}{g'(1)}=\dfrac{2*5*(3*(-3)+1)}{2}\\\\=5*(-9+1)\\\\=5*(-8)\\\\=\boxed{-40}[/tex]
Thank you.
If a 1000-count bottle of omeprazole 40 mg capsules costs the pharmacy $42.88, what is the estimated cost per capsule, rounded
to the nearest penny?
Answer:
Estimated cost per capsule = 4.288 (penny)
Step-by-step explanation:
Given:
Cost of 1000 capsule = $42.88
Number of capsules = 1000
Find:
Estimated cost per capsule
Computation:
1 dollar = 100 penny
So,
$42.88 = 4288 penny
Estimated cost per capsule = 4288 / 1000
Estimated cost per capsule = 4.288 (penny)
851-473 is the same as (_)-378...
What is working to get the answer in the parentheses?
Answer:
851- 473 = 373
(751)-378 = 373
33505 divide 160 in fraction
Answer: The answer is 209.40625
The fractional equivalent of 33505 divided by 160 is 6701/32 .
Given,
33505/160
Now,
To get the fractional equivalent of 33505/160,
Divide numerator and denominator by the common factor .
So divide numerator and denominator by 5.
33505/5 = 6701
160/5 = 32
Now the simplified fraction is 6701/32.
Know more about fractions,
https://brainly.com/question/10354322
#SPJ6
Solve the system algebraically.
3x - 2y - 1 = 0 y = 5x + 4
What is the solution?
A:{(-9/7,-17/7)}
B:{(9/7.17/7)}
C:{(9/7,-17-7)}
Answer:
A:{(-9/7,-17/7)}
Step-by-step explanation:
3x - 2y - 1 = 0 ⇒ 3x - 2y = 1
y = 5x + 4
then:
3x - 2(5x+4) = 1
3x - 2*5x - 2*4 = 1
3x - 10x - 8 = 1
-7x = 1 + 8
7x = 9
x = -9/7
y = 5x + 4
y = 5(-9/7) + 4
y = -45/7 + 4
y = -45/7 + 28/7
y = -17/7
Answer:
A:{(-9/7, -17/7)}
The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes. Find the probability that a call a. lasts between 5 and 10 minutes. b. lasts more than 7 minutes. c. lasts less than 4 minutes.
Answer: a. 0.6759 b. 0.3752 c. 0.1480
Step-by-step explanation:
Given : The long-distance calls made by the employees of a company are normally distributed with a mean of 6.3 minutes and a standard deviation of 2.2 minutes
i.e. [tex]\mu = 6.3[/tex] minutes
[tex]\sigma=2.2[/tex] minutes
Let x be the long-distance call length.
a. The probability that a call lasts between 5 and 10 minutes will be :-
[tex]P(5<X<10)=P(\dfrac{5-6.3}{2.2}<\dfrac{X-\mu}{\sigma}>\dfrac{10-6.3}{2.2})\\\\=P(-0.59<Z<1.68)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=P(z<1.68)-(1-P(z<0.59))\\\\=0.9535-(1-0.7224)\ \ \ \ [\text{by z-table}]\\\\=0.6759[/tex]
b. The probability that a call lasts more than 7 minutes. :
[tex]P(X>7)=P(\dfrac{X-\mu}{\sigma}>\dfrac{7-6.3}{2.2})\\\\=P(Z>0.318)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<0.318)\\\\=1-0.6248\ \ \ \ [\text{by z-table}]\\\\=0.3752[/tex]
c. The probability that a call lasts more than 4 minutes. :
[tex]P(X<4)=P(\dfrac{X-\mu}{\sigma}<\dfrac{4-6.3}{2.2})\\\\=P(Z<-1.045)\ \ \ \ [z=\dfrac{X-\mu}{\sigma}]\\\\=1-P(Z<1.045)\\\\=1-0.8520 \ \ \ [\text{by z-table}]\\\\=0.1480[/tex]
The derivative of the trigonometric function. Please help me.
[tex]y=\dfrac{sin(x^2)}{x^3}[/tex]
Apply the quotient rule:
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{x^3\frac{\mathrm d\sin(x^2)}{\mathrm dx}-\sin(x^2)\frac{\mathrm dx^3}{\mathrm dx}}{(x^3)^2}[/tex]
Chain and power rules:
[tex]\dfrac{\mathrm d\sin(x^2)}{\mathrm dx}=\cos(x^2)\dfrac{\mathrm dx^2}{\mathrm dx}=2x\cos(x^2)[/tex]
Power rule:
[tex]\dfrac{\mathrm dx^3}{\mathrm dx}=3x^2[/tex]
Putting everything together, we have
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{x^3(2x\cos(x^2))-\sin(x^2)(2x\cos(x^2))}{(x^3)^2}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x^3\cos(x^2)-2x\sin(x^2)\cos(x^2)}{x^6}[/tex]
[tex]\dfrac{\mathrm dy}{\mathrm dx}=\dfrac{2x^2\cos(x^2)-\sin(2x^2)}{x^5}[/tex]
When [tex]x=\sqrt{\frac\pi2}[/tex], we have
[tex]\cos\left(\left(\sqrt{\dfrac\pi2}\right)^2\right)=\cos\left(\dfrac\pi2\right)=0[/tex]
[tex]\sin\left(2\left(\sqrt{\dfrac\pi2}\right)^2\right)=\sin(\pi)=0[/tex]
so the derivative is 0.
a jogger runs at an average speed of six miles per hour. At that rate, how far will the jogger travel in one and one half hours?
Answer:
9 miles
Step-by-step explanation:
Hour = 6 miles
Half an hour = 3
6 + 3 = 9
all the factors of 6
Answer:
1, 2, 3 and 6.
Step-by-step explanation:
Factors of 6 are 1, 2, 3 and 6.
Find the mode. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The mode(s) is(are) nothing. (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.) B. There is no mode.
Answer:
The question is not complete, but I found a possible match:
Find the (a) mean, (b) median, (c) mode, and (d) midrange for the data and then (e) answer the given question. Listed below are the jersey numbers of 11 players randomly selected from the roster of a championship sports team. What do the results tell us?
86 4 85 83 9 51 24 34 28 43
Find the mode. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
A. The mode(s) is(are) nothing. (Type an integer or a decimal. Do not round. Use a comma to separate answers as needed.)
B. There is no mode.
Answer:
The correct answer is:
There is no mode (B.)
Step-by-step explanation:
b. The mode of data is the number that repeats the most number of times. The number that occurs most frequently. on the list of the distribution, 86 4 8 5 83 9 51 24 34 28 43, every number occurs just once, hence, there is no mode for the distribution.
a. To calculate the Mean
[tex]Mean: \frac{Sum\ of\ terms}{number\ of\ players}\\ Mean = \frac{86\ +\ 4\ +\ 8\ +\ 5\ +\ 83\ +\ 9\ +\ 51\ +\ 24\ +\ 34\ +\ 28\ +\ 43}{11}\\Mean= 34.09[/tex]
c. To calculate the median:
Median is the mid-way term of the distribution, but first, we have to arrange the terms in ascending order (descending order can also be used)
4, 5, 8, 9, 24, 28, 34, 43, 51, 63, 86
To find the median, count the numbers equally from the left- and right-hand sides to the middle, the remaining number becomes the median. In this case, the median = 28
d. Midrange:
The midrange is the number mid-way between the greatest and smallest number in a data set. To find the midrange, we will add the smallest (4) and largest number (86), and divide by 2:
Midrange = (4 + 86) ÷ 2
Midrange = 90 ÷ 2 = 45
e. what do the results tell us:
Since only 11 of the jersey numbers were in the sample, the statistics cannot give any meaningful results